Computing the multiplicity structure of an isolated singular solution: Case of breadth one

We present an explicit algorithm to compute a closed basis of the local dual space of I=(f1,…,ft) at a given isolated singular solution xˆ=(xˆ1,…,xˆs) when the Jacobian matrix J(xˆ) has corank one. The algorithm is efficient both in time and memory use. Moreover, it can be modified to compute an approximate basis if the coefficients of f1,…,ft and xˆ are only known with limited accuracy.